Q. If $G$ is the centroid of the $\mathrm{\Delta}\ ABC,$ then $\overrightarrow{\mathbf{GA}} + \overrightarrow{\mathbf{BG}} + \overrightarrow{\mathbf{GC}}$ is equal to
A) $2\overrightarrow{\mathbf{GB}}$
B) $2\overrightarrow{\mathbf{GA}}$
C) $\overrightarrow{\mathbf{0}}\$
D) $2\overrightarrow{\mathbf{BG}}$
Explanation
(d)
Since, $G$ is the centroid of a triangle, then
$\overrightarrow{\mathbf{GA}} + \overrightarrow{\mathbf{GB}} + \overrightarrow{\mathbf{GC}} = \overrightarrow{\mathbf{0}}\ \Longrightarrow \overrightarrow{\mathbf{GA}} + \overrightarrow{\mathbf{GC}} = - \overrightarrow{\mathbf{GB}}\ldots.(i)$
Now, $\overrightarrow{\mathbf{GA}} + \overrightarrow{\mathbf{BG}} + \overrightarrow{\mathbf{GC}} = - \overrightarrow{\mathbf{GB}} + \overrightarrow{\mathbf{BG}} = 2\overrightarrow{\mathbf{BG}}$
[ from Eq. (i)]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.